2019-03-16T15:54:04ZPreferential accessibility and preferred worldshttp://hdl.handle.net/10204/10767
Preferential accessibility and preferred worlds
Britz, K; Varzinczak, I
Modal accounts of normality in non-monotonic reasoning traditionally have an underlying semantics based on a notion of preference amongst worlds. In this paper, we motivate and investigate an alternative semantics, based on ordered accessibility relations in Kripke frames. The underlying intuition is that some world tuples may be seen as more normal, while others may be seen as more exceptional. We show that this delivers an elegant and intuitive semantic construction, which gives a new perspective on defeasible necessity. Technically, the revisited logic does not change the expressive power of our previously defined preferential modalities. This conclusion follows from an analysis of both semantic constructions via a generalisation of bisimulations to the preferential case. Reasoners based on the previous semantics therefore also suffice for reasoning over the new semantics. We complete the picture by investigating different notions of defeasible conditionals in modal logic that can also be captured within our framework.
Copyright: 2018 Springer. Due to copyright restrictions, the attached PDF file only contains the abstract of the full text item. For access to the full text item, please consult the publisher's website: https://doi.org/10.1007/s10849-017-9264-0. A free fulltext non-print version of the article can be viewed at https://rdcu.be/bpFi0
2018-06-01T00:00:00ZThe output size problem for string-to-tree transducershttp://hdl.handle.net/10204/10756
The output size problem for string-to-tree transducers
Berglund, Martin; Drewes, F; Van der Merwe, B
The output size problem, for a string-to-tree transducer, is to determine the asymptotic behavior of the function describing the maximum size of output trees, with respect to the length of input strings. We show that the problem to determine, for a given regular expression, the worst-case matching time of a backtracking regular expression matcher, can be reduced to the output size problem. The latter can, in turn, be solved by determining the degree of ambiguity of a non-deterministic finite automaton.
Due to copyright restrictions, the attached PDF file contains the accepted version of the published item. The article may be used for non-commercial purposes only.The definitive version is published in Journal of Automata, Languages and Combinatorics. For access to the published version, kindly consult the publisher's website: https://www.jalc.de/issues/2018/issue_23_1-3/jalc-2018-019-038.php
2018-04-01T00:00:00ZFrom KLM-style conditionals to defeasible modalities, and backhttp://hdl.handle.net/10204/10755
From KLM-style conditionals to defeasible modalities, and back
Britz, K; Varzinczak, I
We investigate an aspect of defeasibility that has somewhat been overlooked by the nonmonotonic reasoning community, namely that of defeasible modes of reasoning. These aim to formalise defeasibility of the traditional notion of necessity in modal logic, in particular of its different readings as action, knowledge and others in specific contexts, rather than defeasibility of conditional forms. Building on an extension of the preferential approach to modal logics, we introduce new modal operators with which to formalise the notion of defeasible necessity and distinct possibility, and that can be used to represent expected effects, refutable knowledge, and so on. We show how KLM-style conditionals can smoothly be integrated with our richer language. We also propose a tableau calculus which is sound and complete with respect to our modal preferential semantics, and of which the computational complexity remains in the same class as that of the underlying classical modal logic.
Copyright: 2018 Taylor & Francis. Due to copyright restrictions, the attached PDF file contains the postprint version of the published item. For access to the published version, kindly consult the publisher's website: https://www.tandfonline.com/doi/full/10.1080/11663081.2017.1397325
2018-03-01T00:00:00ZA semantic perspective on belief change in a preferential non-monotonic frameworkhttp://hdl.handle.net/10204/10749
A semantic perspective on belief change in a preferential non-monotonic framework
Casini, G; Ferme, E; Meyer, T; Varzinczak, I
Belief change and non-monotonic reasoning are usually viewed as two sides of the same coin, with results showing that one can formally be defined in terms of the other. In this paper we investigate the integration of the two formalisms by studying belief change for a (preferential) non-monotonic framework. We show that the standard AGM approach to belief change can be transferred to a preferential non-monotonic framework in the sense that change operations can be defined on conditional knowledge bases. We take as a point of departure the results presented by Casini and Meyer (2017), and we develop and extend such results with characterisations based on semantics and entrenchment relations, showing how some of the constructions defined for propositional logic can be lifted to our preferential non-monotonic framework.
Paper presented at the 16th International Conference on Principles of Knowledge Representation and Reasoning, Tempe, Arizona, USA, 30 October 2018 - 2 November 2018
2018-10-01T00:00:00Z